Stabilization using fractional-order PI and PID controllers

This paper presents a solution to the problem of stabilizing a given fractional dynamic system using fractional-order PI lambda and (PID mu)-D-lambda controllers. It is based on plotting the global stability region in the (k(p), k(i))plane for the PI lambda controller and in the (k(p), k(i), k(d))-space for the (PID mu)-D-lambda controller. Analytical expressions are derived for the purpose of describing the stability domain boundaries which are described by real root boundary, infinite root boundary and complex root boundary. Thus, the complete set of stabilizing parameters of the fractional-order controller is obtained. The algorithm has a simple and reliable result which is illustrated by several examples, and hence is practically useful in the analysis and design of fractional-order control systems.